Question

A diver who has a mass of 68 kg climbs to a diving platform that is 7.5 m above the surface of a pool. How much gravitational potential energy does the diver have in relation to the pool’s surface?

510 J
1912 J
3825 J
4998 J

Answer 1

The gravitational potential energy (PE) can be calculated using the formula:

\[
PE = m \cdot g \cdot h
\]

where:
- \( m \) is the mass in kilograms,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height in meters above the reference point (in this case, the pool's surface).

Plugging in the values:

- \( m = 68 \, \text{kg} \)
- \( g = 9.81 \, \text{m/s}^2 \)
- \( h = 7.5 \, \text{m} \)

Now, substituting these values into the formula:

\[
PE = 68 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 7.5 \, \text{m}
\]

Calculating it step-by-step:

1. \( 68 \cdot 9.81 = 667.08 \, \text{N} \)
2. \( 667.08 \cdot 7.5 = 5003.1 \, \text{J} \)

Thus, the gravitational potential energy is approximately \( 5003.1 \, \text{J} \).

Rounding this to closely match the given options, the answer is:

**4998 J** (This is the correct option that is closest to our calculated value.)